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Distill n' Explain: explaining graph neural networks using simple surrogates

Tamara Pereira, Erik Nascimento, Lucas E. Resck, Diego Mesquita, Amauri Souza

TL;DR

This work proposes Distill n' Explain (DnX), a faster version of DnX that leverages the linear decomposition of the authors' surrogate model and supports the empirical findings with theoretical results linking the quality of the surrogate model to the faithfulness of explanations.

Abstract

Explaining node predictions in graph neural networks (GNNs) often boils down to finding graph substructures that preserve predictions. Finding these structures usually implies back-propagating through the GNN, bonding the complexity (e.g., number of layers) of the GNN to the cost of explaining it. This naturally begs the question: Can we break this bond by explaining a simpler surrogate GNN? To answer the question, we propose Distill n' Explain (DnX). First, DnX learns a surrogate GNN via knowledge distillation. Then, DnX extracts node or edge-level explanations by solving a simple convex program. We also propose FastDnX, a faster version of DnX that leverages the linear decomposition of our surrogate model. Experiments show that DnX and FastDnX often outperform state-of-the-art GNN explainers while being orders of magnitude faster. Additionally, we support our empirical findings with theoretical results linking the quality of the surrogate model (i.e., distillation error) to the faithfulness of explanations.

Distill n' Explain: explaining graph neural networks using simple surrogates

TL;DR

This work proposes Distill n' Explain (DnX), a faster version of DnX that leverages the linear decomposition of the authors' surrogate model and supports the empirical findings with theoretical results linking the quality of the surrogate model to the faithfulness of explanations.

Abstract

Explaining node predictions in graph neural networks (GNNs) often boils down to finding graph substructures that preserve predictions. Finding these structures usually implies back-propagating through the GNN, bonding the complexity (e.g., number of layers) of the GNN to the cost of explaining it. This naturally begs the question: Can we break this bond by explaining a simpler surrogate GNN? To answer the question, we propose Distill n' Explain (DnX). First, DnX learns a surrogate GNN via knowledge distillation. Then, DnX extracts node or edge-level explanations by solving a simple convex program. We also propose FastDnX, a faster version of DnX that leverages the linear decomposition of our surrogate model. Experiments show that DnX and FastDnX often outperform state-of-the-art GNN explainers while being orders of magnitude faster. Additionally, we support our empirical findings with theoretical results linking the quality of the surrogate model (i.e., distillation error) to the faithfulness of explanations.
Paper Structure (36 sections, 5 theorems, 26 equations, 3 figures, 11 tables)

This paper contains 36 sections, 5 theorems, 26 equations, 3 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Notation.
  4. Graph neural networks (GNNs).
  5. DnX: Distill n' Explain
  6. Knowledge distillation
  7. Explanation extraction
  8. Optimizing for $\mathcal{E}$.
  9. Finding $\mathcal{E}$ via linear decomposition.
  10. Analysis
  11. Additional related works
  12. Explanations for GNNs.
  13. Knowledge distillation.
  14. Experiments
  15. Experimental setup
  16. ...and 21 more sections

Key Result

Lemma 1

Given a node $u$ and a set $\mathcal{K}$ of perturbations, the unfaithfulness of the explanation $\mathcal{E}_u$ with respect to the prediction $Y_u^{(\Psi_\Theta)}$ of node $u$ is bounded as follows: where $\mathcal{G}_{u}^\prime$ is a possibly perturbed version of $\mathcal{G}_u$, $t$ is a function that applies the explanation $\mathcal{E}_u$ to the graph $\mathcal{G}_{u}^\prime$, $\gamma$ is a

Figures (3)

  • Figure 1: Time comparison. The bar plots show the average time each method takes to explain a prediction from GCN. FastDnX is consistently the fastest method, often by a large margin. For the datasets with largest average degree (Bitcoin datasets), FastDnX is 4 orders of magnitude faster than PGMExplainer and 2 orders faster than the other methods.
  • Figure 2: Confusion matrix of the distillation process for the BA-Community dataset. Classes 1 and 5 correspond to base nodes. While the surrogate misclassifies many motif nodes, it is able to correctly predict almost all base ones.
  • Figure 3: Degree distribution of motif and base nodes. While we can overall distinguish motif and base nodes from degree information on BA-based datasets, there is a significant overlap on Tree-Cycles and Tree-Grids.

Theorems & Definitions (11)

  • Definition 1: Faithfulness
  • Lemma 1: Unfaithfulness with respect to $\Psi$
  • proof : Sketch of the proof.
  • Theorem 1: Unfaithfulness with respect to $\Phi$
  • Lemma 2: Probability bound on unfaithfulness w.r.t. $\Psi$
  • Theorem 2: Probability bound on unfaithfulness w.r.t. $\Phi$
  • Theorem 3: Convexity of DnX
  • proof : Proof of Lemma \ref{['theo:bound_unfaithfulness']}
  • proof : Proof of Theorem \ref{['theo:bound_unfaithfulness_2']}
  • proof : Proof of Lemma \ref{['theo:prob_bound_unfaithfulness']}
  • ...and 1 more